Finally, we demonstrate the revival of Gaussian EPR steering by establishing
a correlated noisy channel, where an auxiliary channel carrying on the noise
correlated with that of the noisy channel is introduced. In today's
communication system, it is relevant to consider channels with correlated
noise (i.e. non-Markovian environment), because the time and space
correlated noise exist naturally  [1]}, , [2]}. Furthermore, it has been experimentally found
that correlated noisy channel can be established by two bounded fibers [3]}, thus the method we use in experiment to built the
non-Markovian environment is applicable and practical significant. As shown
in Fig. 1b. The auxiliary noisy channel based on an ancillary coherent state
\(\hat{c}_{an}\) , which is modulated to carry the noise information correlated
with that in the noisy quantum channel, saying \(\hat{c}_{an}^{\prime }=\hat{c}_{an}+\sqrt{g_{an}}\hat{N}\)  (\(g_{an}\)  is the magnitude of the correlated
noise and is experimentally adjustable). Thus there exists correlation
between the quantum system and environment. The noisy transmitted mode \(\hat{B}_{N}\)  couples with the auxiliary noisy channel on a revival beam-splitter
with transmission efficiency \(T\) . One of the output mode we need from the
revival beam-splitter is \(\hat{B}_{R}=\sqrt{\eta _{N}T}\hat{B}+\sqrt{\left(1-\eta _{N}\right) gT}\hat{N}-\sqrt{\left( 1-T\right) g_{an}}\hat{N}+\sqrt{\left( 1-\eta _{N}\right) T}\hat{v}-\sqrt{1-T}\hat{c}_{an}\) , when the
adjustable \(g_{an}\)  and \(T\)  satisfy
\(\frac{g}{g_{an}}=\frac{1-T}{\left( 1-\eta _{N}\right) T}, \) 
